When the last three are the main pressure points of the grip, the thumb and index never come into play. The thumb doesn't cross or grab on to the third finger. With this grip, the thumb and index finger are lightly around the cue, with the thumb maybe barely touching the third finger, but certainly not wrapped around it. In the follow through position, the thumb and index finger are laying parallel alongside the cue. Having the thumb and index finger face downward is more of an exercise to get used to taking the pressure off of those two fingers, but not necessary, once you've mastered the pressure points of that grip.
Now, as to why --- a few reasons. First, the index and the thumb are the twisting fingers. If you're going to twist your cue, it will be with those two. Many players have found a way of avoiding the twist with those two, but it's not exactly a natural hand position and doesn't move naturally with the cue.
Using the last three, keeps the hand in it's most natural position as the cue moves through the stroke. It also facilitates the concept of shooting with your arm rather than with your hand. Unless you're doing something special which you're not most of the time, your grip should do nothing more than hold on to the cue without twisting it, and move naturally with it.
The pinkie is the anchor and the extension of your arm. Taking it off the cue makes your grip hand more flexible. That works if you need to snap your cue, or as the players of the older times --- used to stand tall, and needed wrist movement for speed due to their limited arm swings. It also works well in short shots in 14.1 where you need power but don't have the room for a big stroke. But these days, with players standing low, pinkie off is more of a weapon in your arsenal than part of your regular grip.
Sometimes things get passed down that aren't needed anymore if you question them.
extremley underestimated fact
few issues- from time to time just reading. same old stories here, hehe. hope all is ok as well on your side.